A Hermite FE method for Maxwell’s equations

This work addresses a novel technique to solve electro-magnetic field problems based on Hermite finite-element interpolations in both two- and three-dimensional space. Method’s basic feature is the use as degrees of freedom of electric field’s normal derivative mean values across the edges or the faces of a mesh consisting of N-simplices, in addition to the field’s mean value in the mesh elements. Second-order convergence in the mean-square sense holds for the electric field, while the magnetic field is at least first-order convergent in the same sense. Numerical results in two dimensions suggest that second-order convergence in the mean-square sense can also be expected of the magnetic field.